Let R be a commutative ring with identity and M be unitary (left) R-module. The principal aim of this paper is to study the relationships between relatively cancellation module and multiplication modules, pure submodules and Noetherian (Artinian) modules.

DBNRAAK Mohammed, International Journal of Research in Social Sciences and Humanities, 2020

MT Suhail, SA Hussein, MN Abdulhussein, WQ Abdaullateef, M khairallah Aid…, Migration Letters, 2024

Gaslift reactors are employed in several bioapplications due to their characteristics of cost-effectiveness and high efficiency. However, the nutrient and thermal gradient is one of the obstacles that stand in the way of its widespread use in biological applications. The diagnosis, analysis, and tracking of fluid paths in external draft tube gaslift bioreactor-type are the main topics of the current study. Several parameters were considered to assess the mixing efficiency such as downcomer-to-rizer diameter ratio (Ded/Dr), the position of the diffuser to the height of bioreactor ratio (Pd/Lr), and gas bubble size (Db). The multiple regression of liquid velocity indicates the optimal setting: Ded/Dr is (0.5), Pd/Lr is (0.02), and Db

<p>The objective of this paper is to study the dynamical behavior of an aquatic food web system. A mathematical model that includes nutrients, phytoplankton and zooplankton is proposed and analyzed. It is assumed that, the phytoplankton divided into two compartments namely toxic phytoplankton which produces a toxic substance as a defensive strategy against predation by zooplankton, and a nontoxic phytoplankton. All the feeding processes in this food web are formulating according to the Lotka-Volterra functional response. This model is represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability

This research deals with Salinger's concerns about predicaments of youth like Franny and her brother Zooey. Their predicaments are related to identity, family, religion, beliefs, life and death, education, source of power, and society. It illustrates adults struggle to adapt themselves to live a normal social American life. It proves necessary to balance their coexistence in a materialistic milieu to achieve spiritual peace, tranquility, and stability.

The research deals with an important detail of the joints of the film industry and television drama, which is the expression and aesthetic of the long shot, after being popularized by some directors, and that the long shot has been employed since the beginning of the cinema. But the research addresses the contemporary film and how the long shot worked. The researcher identified her goal in identifying the aesthetic and expressive of the long shot in the contemporary film, and then defined the term of the shot and the long shot.
The theoretical framework was based on two topics: the first (aesthetic and artistic expression in cinema) and the second (the long shot and the state of its construction). The researcher then chose LA LA LAND

Two means used for saving fish samples, namely Freezing and Preservatives represented by Alcohol and Formalin. The Freezing was used in saving samples collected newly, in addition to use Alcohol and Formalin with different concentrations 70% of Alcohol and 10% of Formalin. The concentrations of some heavy metal elements were examined, such as Potassium, Phosphorus, Calcium, Manganese, Magnesium, Zinc, Iron, Copper and Boron in samples saved in Formalin and Alcohol and frozen at different durations. The concentration of some elements has been changed during the saving duration. The study was performed on the concentration of heavy elements in the Liza abu muscles of saved and frozen fish.